2740: Square Packing

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Square Packing

Title text: I also managed to improve the solution for n=1 to s<0.97, and with some upgrades I think I can hit 0.96.

Explanation

This explanation may be incomplete or incorrect: Created by a HYDRAULIC PRESSED SQUARE - This appears to be referring to a specific puzzle that merits explanation before going into description of the comic. Do NOT delete this tag too soon. If you can address this issue, please edit the page! Thanks.

Herein, Randall claims to have found a more efficient 11-square packing for the square packing in a square problem, by physically deforming the squares involved with a hydraulic press. Geometrical shapes in packing problems are not conventionally assumed to be deformable in this manner.^{[citation needed]}

Transcript

This transcript is incomplete. Please help editing it! Thanks.

[11 squares optimally packed inside a square arrangement]

Previous best

s<3.877084

(Gensane, 2004)

[11 deformed squares crushed together to pack them into a smaller square arrangement]

New record

s<3.40

[Caption below the panel:]

I've significantly improved on the solution to the n=11 square packing problem by using a hydraulic press.

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Discussion

I suspect Randall saw the same social media post that I did (or maybe a repost of the same social media post, who knows or cares). I don't really want to make an explanation, but anyone who does, here's a link to a bunch of square packing findings... of course, no hydraulic press allowed for these packings. https://erich-friedman.github.io/packing/squinsqu/ Tsumikiminiwa (talk) 22:07, 20 February 2023 (UTC)

Yeah, this was on r/mathmemes the other day. 172.64.238.48 00:03, 21 February 2023 (UTC)

Welcome to the Hydraulic Press Channel. Today we have a set of squares that are usually used in packing problems. You are supposed to fit them into other squares by arranging them. But I think we can get them to fit easier if we put them on the press, and just try to make them smaller. We are going to start with one square, and see how much smaller we can make this. And here we go.

Needs to include a mention of the "Square Packer Five Meeellion"... 172.68.51.141 16:48, 21 February 2023 (UTC)

The post where I saw this said: “God is dead, and what killed him was learning [the similarly inelegant-appearing n=17 solution].” 172.70.254.216 13:08, 21 February 2023 (UTC)

172.70.54.77 19:26, 21 February 2023 (UTC) Welcome to the Hydraulic Press channel

What does "s<" mean? Kev (talk) 22:54, 21 February 2023 (UTC)

"S" (the size of the square, within which lie the N small squares) is less than the following number. i.e. that any S of that amount or greater is more than enough space to contain N unit squares. But it isn't fully established what the smallest value of S is, just that it will not be bigger than (or equal to) that provisional limit.

(Do we need a wikilink to inequality notation in the explanation, then? Maybe you can tell us, Kev.) 172.71.242.191 23:17, 21 February 2023 (UTC)

Please! I came to the discussion to ask that an explanation of what s means. I did have a look in the Wikipedia article about it, but they don't use it there. So an explanation in the text with perhaps a link to something that expands on the explanation would be greatly appreciated by me :-) 172.70.91.198 12:45, 22 February 2023 (UTC)

Added something about this. Seems too wordy and partly a repeat of the above. Future editors will refine, no doubt. 141.101.98.77 19:43, 22 February 2023 (UTC)

Well, I had added it. Someone rewrote it and it now just says something not at all what the above people wanted it to say... Go figure... 172.70.90.35 01:10, 23 February 2023 (UTC)

Is there a solution to the problem of the smallest explanation into which n explanations can be packed? 172.70.90.35 11:29, 23 February 2023 (UTC)

Probably, that's [one of] the issue[s] addressed by compression algorithms. 172.70.114.88 23:26, 26 February 2023 (UTC)

I think I saw this new solution in a paper authored by USPS et al. 108.162.216.159 23:33, 21 February 2023 (UTC)

I believe we can get S<3.32 for this problem... if it will Blend. --172.69.79.133 09:28, 22 February 2023 (UTC)

Assuming that when Randall says "some upgrades", he means the strongest hydraulic press humanity has created, what would be the compressive strength of the square in the title text? ~ Megan ^she/_her ^talk/_contribs 01:57, 23 February 2023 (UTC)

First time I've seen a citation in an Explain XKCD explanation, LOL! And if I haven't read all 2740 up until here, I'm close (MAYBE the first few hundred I skipped the explanation if I understood the comic). :) NiceGuy1 (talk) 05:07, 26 February 2023 (UTC)

I'm on mobile so can't easily edit it myself but I think the reference to 11 square packing in 2765: escape speed should be linked to here :) 162.158.34.23 11:37, 29 September 2023 (UTC)